Hardness of approximating the shortest vector problem in lattices

@article{Khot2004HardnessOA,
  title={Hardness of approximating the shortest vector problem in lattices},
  author={Subhash Khot},
  journal={45th Annual IEEE Symposium on Foundations of Computer Science},
  year={2004},
  pages={126-135}
}
  • Subhash Khot
  • Published 2004
  • Mathematics, Computer Science
  • 45th Annual IEEE Symposium on Foundations of Computer Science
Let p > 1 be any fixed real. We show that assuming NP /spl nsube/ RP, it is hard to approximate the shortest vector problem (SVP) in l/sub p/ norm within an arbitrarily large constant factor. Under the stronger assumption NP /spl nsube/ RTIME(2/sup poly(log n)/), we show that the problem is hard to approximate within factor 2/sup log n1/2 - /spl epsi// where n is the dimension of the lattice and /spl epsi/> 0 is an arbitrarily small constant. This greatly improves all previous results in l/sub… Expand
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